强言闭群的有限正则子群

Pub Date : 2024-02-13 DOI:10.1515/jgth-2023-0015

Filipp D. Denissov

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引用次数: 0

摘要

A. A. Klyachko、V. Y. Miroshnichenko 和 A. Y. Olshanskii 最近的一篇论文证明，任何有限强言闭群的中心都是直接因子。在本文中，我们将这一结果扩展到任何强言闭群的有限正则子群的情况。由此可知，具有非阿贝尔扭转子群的有限生成零能群不是强封闭群。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Finite normal subgroups of strongly verbally closed groups

In a recent paper by A. A. Klyachko, V. Y. Miroshnichenko, and A. Y. Olshanskii, it is proven that the center of any finite strongly verbally closed group is a direct factor. In this paper, we extend this result to the case of finite normal subgroups of any strongly verbally closed group. It follows that finitely generated nilpotent groups with nonabelian torsion subgroups are not strongly verbally closed.

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